Since the trace A+C can never be zero for an ellipse, the arbitrary
scale factor in the coefficients of the conic equation can be naturally
removed by the normalization A+C=1. This normalization has been used
by many researchers [17, 21].
All ellipse can then be described by a 5-vector

and the system equation becomes:

where

Given n points, we have the following vector equation:

where

The function to minimize becomes

Obtaining its partial derivative with respect to and
setting it to zero yield: